Solution of Triangles SINE RULE. 22 angle dan 1 side are given e.g  A = 60 ,  B = 40  and side b = 8 cm then, side a & side c can be found using.

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Solution of Triangles SINE RULE

22 angle dan 1 side are given e.g  A = 60 ,  B = 40  and side b = 8 cm then, side a & side c can be found using sine rule; B A C a b c 8cm 60  40  1 2 =10.78= ° How much is angle C?

SINE RULE → 2 sides and 1 non-included angle given. example; a= 8, b= 10cm and  B=70  then we can find  A,  C and side c using sine rule. B A C a b c 8 cm 10 cm 70°  C = 180° - 70° - 48°45’ = 61° 15’ = 9.33 cm

Practice 1 Find (a) length AC (b) length BC AC = cm  A = 180 – 45 – 59 = 76  BC = cm

Ambiguous What does am-big-u-ous mean? 1. Open to more than one interpretation 2. Doubtful or Uncertain. Ambiguous indicates the presence of two or more possible meanings.

Ambiguous Case When length of 2 sides and one non-included acute angle are given, e.g  A, side c and a. Þ2Þ2 possible triangle can be drawn:  ABC or  ABC’ where BC = BC’ A B C C’ c a a

Example ABC is a triangle with  A = 28 , AB = 14 cm and BC = 9 cm. Solve the triangle. 2 possible triangle can be formed. There are 2 possible solution for each sides and angle to be solved. C’ A B C 14 cm9 cm 28  9 cm

A B C 14 cm9 cm C’ 28  9 cm Example C = sin -1 0,7303 = 46  55’ or 133  5’  ACB = 46  55’  AC’B = 133  5’  ABC = 180  – 28  – 46  55’ = 105  5’  ABC’ = 180  – 28  – 133  5’ = 18  55’ AC = AC = 6.215

Exercise (Ambiguous case) Given a triangle ABC, the length of AB = 8 cm, BC = 7 cm, and  A = 48°. Find  B,  C and the length of AC Answer:  B = 73°52’, 10° 8’  C = 58°8’,121° 52’ AC = 9.04 cm, 1.66 cm